Date of Award

Winter 2012

Project Type

Thesis

Program or Major

Mechanical Engineering

Degree Name

Master of Science

First Advisor

Joseph Klewicki

Abstract

Correlations between specific velocity and vorticity components dictate how the distributions of mean momentum and turbulence kinetic energy are realized in the turbulent boundary layer. For turbulent inertia to remain dynamically significant at arbitrarily high Reynolds number, differences of these correlations must remain non-zero. This motivates the study of velocity vorticity products under the influence of increasing scale separation. Through the use of both laboratory and field data, scale separation between relevant velocity and vorticity components is shown to increase with distance from the wall and Reynolds number. Time-delayed correlations between the vertical velocity and spanwise vorticity fluctuations reveal that only very slight variations in their average phase relation would cause significant variations in the mean transport of momentum. Spectral analyses are used to explore previous observations of scale selection between the participating velocity and vorticity cornponents. The wavelengths corresponding to the peaks in the relevant velocity and vorticity component spectra are used to describe scale separation effects. The variations in the wavelength ratios are shown to correlate with the scaling properties that follow from the magnitude ordering of terms in the mean momentum equation. Scale separation is observed to arise via spatial confinement, and spatial dispersion. In the region where the mean viscous force is of leading order, the mechanism of vortex stretching generates motions bearing concentrated vorticity that, with increasing Reynolds number, are confined to a smaller fraction of the viscous region flow volume. In the region where the mean dynamics are inertially dominated, the characteristic vortical motions are sparsely dispersed over a domain whose thickness asymptotically grows like the boundary layer thickness. In the region y + ≲ 40, the streamwise lengths of the correlations affiliated with turbulent inertia are seen to scale with the square root of the Reynolds number, while those affiliated with the gradient of turbulence kinetic energy are seen to scale with the Reynolds number itself.

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